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## Homework Statement

Is [tex] f(y)=\sum_{m=1}^\infty \frac{1}{y^2+m^2}

[/tex]differentiable?

## Homework Equations

## The Attempt at a Solution

From the graph, it is obvious that f is not differentiable at y=0, but I don't know how to prove that. I proved that [tex] \sum_{m=1}^n f_m=\sum_{m=1}^n\frac{1}{y^2+m^2} [/tex] converges uniformly to f. Does this help? Thank you very much.